Ubiquitous and mobile context-aware computing is an essential component of the smart cities infrastructure. Widely available wireless networks, the maturity level of distributed computing and the increasing number of mobile devices have significantly influenced the human experience with computing. In the present paper, we discuss the need for a model that will be able to represent a formal structure of a context-aware system in a device. The core functionality of the model is expected to expose context-aware behaviour and support dynamic integration of mobile devices and context-aware behaviour. The major contribution of this work is to identify deficiencies of the existing model which is using the notions from sociology such as Role, Ownership and Responsibility.